PROF. W. H. BRAGG ON X-RAYS AND CRYSTAL STRUCTURE. 263 



The spectra resemble those of zinc blende, except that the odd orders of the (100) 

 spectra and the second order of the (ill) spectra are not merely abnormally small, 

 but have entirely disappeared. These facts are very simply explained. The structure 

 is obtained in exactly the same way as that of zinc blende ; but the two lattices are 

 alike, both being of carbon, and when their influences interfere, the interference is 

 complete. 



Finally, consider the case of fluor-spar (CaF 2 ) for a special reason. 



As regards relative positions and intensities the spectra are exactly the same as 

 those of diamond. If we begin with a face-centred lattice of calcium atoms, we must 

 so move out from it two similar lattices of fluorine atoms as to obtain the observed 

 relative intensities. This we do by moving them along the cube diagonal, but 

 in opposite directions, the distance moved being one quarter of the length of the 

 diagonal. This gives a highly symmetrical structure. A fluorine atom lies at the 

 centre of eacli of the eight cubes into which the large face-centred cube can be 

 divided. The (100) planes of fluorine now lie half-way between the (100) planes of 

 calcium, and we explain the disappearance of the first order (100) spectrum by 

 supposing that they have equal reflecting powers. We assume, in fact, that two 

 fluorine atoms of weight 38 are equivalent, within errors of experiment to one atom 

 of calcium of weight 40. This is only one instance out of many ; it seems certain 

 that two planes containing equal weights per unit area are equivalent in reflecting 

 power, no matter how the weight is made up nor how it is distributed in the plane. As 

 regards distribution, this is what we should expect : as regards the effect of weight 

 the result is not so obvious, though it cannot surprise us if we suppose the scattering 

 to be due to the cumulative effect of the electrons and nuclei of the atoms. 



In the simple cases which we have been considering, the considerations of crystal 

 symmetry, though unable of themselves to determine crystal structure, come so near 

 to doing so that a few plain hints given by the new methods have been sufficient for 

 the completion of the task. The exact positions of the atoms are then known. 



But this is not the case with more complicated crystals. As an example we may 

 take the case of iron pyrites. There is a fundamental face-centred lattice of iron 

 atoms, and sulphur lattices are displaced from it in a manner similar to that which 

 has already been described, yet more complicated. The main point, however, is that 

 the extent qf the movement cannot be determined from symmetry considerations. 

 In the cases described above the exact movement could be told from these con- 

 siderations, as soon as the X-ray method had revealed its nature. But in iron pyrites, 

 and probably in the vast majority of crystals, the movement must be calculated from 

 determinations of the relative intensities of the X-ray spectra. 



We require, therefore, to determine in the first place how they should be measured, 

 and in the second how they are to be interpreted. In what follows I propose to 

 consider these two points, particularly the latter. 



The method of measurement has already been described ('Phil. Mag.,' May, 1914). 



2 M 2 



